Hyperbolic structure and stickiness effect: A case of a 2D area-preserving twist mapping  

作　　者：ZHOU LiYong LI Jian CHENG Jian SUN YiSui 

机构地区：[1]School of Astronomy and Space Sciences, Nanjing University [2]Key Laboratory of Modern Astronomy and Astrophysics in Ministry of Education, Nanjing University [3]Department of Mathematics, Nanjing University

出　　处：《Science China(Physics,Mechanics & Astronomy)》2014年第9期1737-1750,共14页中国科学：物理学、力学、天文学（英文版）

基　　金：supported by the National Natural Science Foundation of China(Grant Nos.11073012,11078001 and 11003008);the Qing Lan Project(Jiangsu Province);the National Basic Research Program of China(Grant Nos.2013CB834103 and 2013CB834904)

摘　　要：The stickiness effect suffered by chaotic orbits diffusing in the phase space of a dynamical system is studied in this paper.Previous works have shown that the hyperbolic structures in the phase space play an essential role in causing the stickiness effect.We present in this paper the relationship between the stickiness effect and the geometric property of hyperbolic structures.Using a two-dimensional area-preserving twist mapping as the model,we develop the numerical algorithms for computing the positions of the hyperbolic periodic orbits and for calculating the angle between the stable and unstable manifolds of the hyperbolic periodic orbit.We show how the stickiness effect and the orbital diffusion speed are related to the angle.The stickiness effect suffered by chaotic orbits diffusing in the phase space of a dynamical system is studied in this paper.Previous works have shown that the hyperbolic structures in the phase space play an essential role in causing the stickiness effect.We present in this paper the relationship between the stickiness effect and the geometric property of hyperbolic structures.Using a two-dimensional area-preserving twist mapping as the model,we develop the numerical algorithms for computing the positions of the hyperbolic periodic orbits and for calculating the angle between the stable and unstable manifolds of the hyperbolic periodic orbit.We show how the stickiness effect and the orbital diffusion speed are related to the angle.

关 键 词：stickiness effect hyperbolic structure stable and unstable manifolds 

分 类 号：O19[理学—数学]